We present the results of a search for second generation leptoquarks S
-2 using 19.3 pb(-1) of data collected at the Collider Detector at Fer
milab (CDF) in p (p) over bar collisions at root s = 1.8 TeV during th
e 1992-93 collider run. We have searched for S-2 (S) over bar(2) pairs
assuming that each leptoquark decays to a muon + quark with a branchi
ng ratio beta. We find two candidate events, consistent with an expect
ed background of 1.11 +/- 0.48. We obtain upper limits on sigma(pp -->
S-2 (S) over bar(2))beta(2) as a function of M(S2). Using a Monte Car
lo prediction for S-2 (S) over bar(2) pair production, we exclude M(S2
) < 131 GeV/c(2) for beta = 1 and M(S2) < 95 GeV/c(2) for beta = 0.5 a
t 95% C.L.